GPGPU Programming for Games and Science

CPU Computing 85

The 0-index roots are the same for the two methods but the 1-index roots

differ. In fact, the roots have trailing significands that differ by seven, which

amounts to a floating-point difference of 1/2

21

+1/2

22

+1/2

23

.

=8.34465e−7.

The pseudocode shows the two floating-point neighbors of the 0-index

root, namely,

rootPrev[0] and rootNext[0]. Observe that the polynomial values

at those points have opposite signs, which means that zero lies between them

(in terms of infinite precision). The polynomial value at the computed root is

nearly zero and has a magnitude smaller than that of the polynomial value

at the root’s next-up neighbor. Thus, the floating-point value computed for

the root is the best that you can do in terms of 32-bit float and polynomi ...